Evolutionary Computing Dialects

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Evolutionary Computing Dialects

• Presented by A.E. Eiben
• Free University Amsterdam
• with thanks to the EvoNet Training Committee and
  its Flying Circus

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Contents

• General formal famework
• Dialects
• genetic algorithms
• evolution strategies
• evolutionary programming
• genetic programming
• Beyond dialects

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General EA Framework

• t 0
• initialize P(0) a1(0), , an(0)
• evaluate F(a1(0)), , F(an(0))
• while (stop(P(t)) ? true)
• recombine P(t) rpar(r)(P(t))
• mutate P(t) mpar(m)(P(t))
• evaluate F(a1(t)), , F(an(t))
• select P(t 1) spar(s)(P(t) ? Q)
• t t 1
• where
• F is the fitness function
• r, m, s are recombination, mutation, selection
  operators
• par(x) contains the paramteres of operator x
• Q is either ? or P(t)

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From framework to dialects

• In theory
• every EA is an instantiation of this framework,
  thus
• specifying a dialect needs only filling in the
  characteristic features
• In practice
• this would be too formalistic
• there are many exceptions (EAs not fitting into
  this framework)

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Genetic algorithm(s)

• Developed USA in the 1970s
• Early names J. Holland, K. DeJong, D. Goldberg
• Typically applied to
• discrete optimization
• Attributed features
• not too fast
• good solver for combinatorial problems
• Special
• many variants, e.g., reproduction models,
  operators
• formerly the GA, nowdays a GA, GAs

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GA representation
Required accuracy determines the of bits to
represent a trait (variable)
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GA crossover (1)

• Crossover is used with probability pc
• 1-point crossover
• Choose a random point on the two parents (same
  for both)
• Split parents at this crossover point
• Create children by exchanging tails
• n-point crossover
• Choose n random crossover points
• Split along those points
• Glue parts, alternating between parents
• uniform crossover
• Assign 'heads' to one parent, 'tails' to the
  other
• Flip a coin for each gene of the first child
• Make an inverse copy of the gene for the second
  child

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GA crossover (2)
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GA mutation

• Mutation
• Alter each gene independently with a probability
  pm
• Relatively large chance for not being mutated
• (exercise L100, pm 1/L)

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GA crossover OR mutation?

• If we define distance in the search space as
  Hamming distance then
• Crossover is explorative, it makes a big jump to
  an area somewhere in between two (parent)
  areas.
• Mutation is exploitative, it creates random small
  variations, thereby staying near the parent.
• To hit the optimum you often need a lucky
  mutation.
• GA community crossover is mission critical.

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GA selection

• Basic idea fitness proportional selection.
• Implementation roulette wheel technique.
• Assign to each individual a part of the roulette
  wheel (size proportional to its fitness).
• Spin the wheel n times to select n individuals.
• Example
• f ? max
• 3 individuals
• f (A) 6, f (B) 5, f (C ) 1

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GA reproduction cycle

• Generational GA model

1. Select parents for the mating pool (size of
mating pool equals population size). 2. Shuffle
the mating pool. 3. For each consecutive pair
apply crossover with probability pc. 4. For each
new-born apply mutation. 5. Replace the whole
population by the mating pool.
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GA Goldberg 89 example (1)
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GA Goldberg 89 example (2)
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Evolution strategies

• Developed Germany in the 1970s
• Early names I. Rechenberg, H.-P. Schwefel
• Typically applied to
• numerical optimization
• Attributed features
• fast
• good optimizer for real-valued optimization
• relatively much theory
• Special
• self-adaptation of (mutation) parameters standard

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ES representation

• Problem optimize f ?n ? ?
• Phenotype space (solution space) ?n
• Genotype space (individual space)
• object values directly (no encoding)
• strategy parameter values
• standard deviations (?s) and
• rotation angles (?s) of mutation
• One individual

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ES mutation (1)

• One step size for each xi (coordinate direction)
• Individual (x1, , xn, ?)
• xi is mutated by adding some ?xi from a normal
  probability distribution
• ? is mutated by a log-normal scheme
  multiplying by e?, with ? from a normal
  distribution
• ? is mutated first ! (why?)

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ES mutation (2)

• Each xi (coordinate direction) has its own step
  size
• Individual (x1, , xn, ?1, , ? n)
• ?0, ?, ? are parameters

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ES mutation (3)
Equal probability to place an offspring
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ES recombination (1)

• Basic ideas
• I? ? I, ? parents yield 1 offspring
• Applied ? times, typically ? gtgt ?
• Applied to object variables as well as strategy
  parameters
• Per offspring gene two corresponding parent genes
  are involved
• Two ways to recombine two parent alleles
• Discrete recombination choose one of them
  randomly
• Intermediate recombination average the values
• Might involve two or more parents (global
  recombination)

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ES recombination (2)

• The standard operator
• For each object variable
• Choose two parents
• Apply discrete recombination on the corresponding
  variables
• For each strategy parameter
• Choose two parents
• Apply intermediate recombination on the
  corresponding parameters
• Global recombination re-choosing the two parents
  for each variable anew (step a above).
• Local recombination same two parents for each
  variable (position i).

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ES recombination (3)
Recombination illustrated
? 3
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ES selection

• Strictly deterministic, rank based
• The ? best ranks are handled equally
• The ? best individuals survive from
• the ? offspring (?, ?) selection
• the parents and the offspring (? ?) selection
• (?, ?) selection often preferred for it is
• important for self-adaptation
• applicable also for noisy objective functions,
  moving optima
• Selective pressure very high

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Evolutionary programming

• Developed USA in the 1960s
• Early names D. Fogel
• Typically applied to
• traditional EP machine learning tasks by finite
  state machines
• contemporary EP (numerical) optimization
• Attributed features
• very open framework any representation and
  mutation ops OK
• crossbred with ES (contemporary EP)
• consequently hard to say what standard EP is
• Special
• no recombination
• self-adaptation of parameters standard
  (contemporary EP)

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Traditional EP Finite State Machines
Initial state C Input string 011101 Output
string 110111 Good predictions 60
Fitnesss prediction capability outputi
inputi1
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EP mutation crossover

• Mutation
• For FSMs change a state-transition, add a state,
  etc.
• For numerical optimization see later
• Crossover none !

representation naturally determines the operators
no crossover between species
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Modern EP representation mutation

• Representation ? x1,,xn, ?1,, ?n ?
• Mutation
• xi is mutated by adding some ?xi from a normal
  probability distribution
• ? is mutated by a normal scheme (ES
  log-normal)
• ?i ?i ? (1 ? ? Ni(0, 1))
• xi xi ?I ? Ni(0, 1)
• ? is mutated first !
• other prob. distributions, e.g., Cauchy, are also
  applied

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EP selection

• Stochastic variant of (? ?)-selection
• P(t) ? parents, P(t) ? offspring
• Selection by conducting pairwise competitions in
  round-robin format
• Each solution x ? P(t) ? P(t) is evaluated
  against q other randomly chosen solutions from
  the population
• For each comparison, a "win" is assigned if x is
  better than its opponent
• The ? solutions with the greatest number of wins
  are retained to be parents of the next generation
• Typically q 10

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Genetic programming

• Developed USA in the 1990s
• Early names J. Koza
• Typically applied to
• machine learning tasks
• Attributed features
• competes with neural nets and alike
• slow
• needs huge populations (thousands)
• Special
• non-linear chromosomes trees, graphs
• mutation possible but not necessary (disputed!)

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GP representation

• Problem domain modelling (forecasting,
  regression, classification, data mining, robot
  control).
• Fitness the performance on a given (training)
  data set, e.g. the nr. of hits/matches/good
  predictions
• Representation implied by problem domain, i.e.
• individual model parse tree
• parse trees sometimes viewed as LISP expressions
  ?
• GP evolving computer programs
• parse trees sometimes viewed as
  just-another-genotype ?
• GP a GA sub-dialect

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GP mutation

• Replace randomly chosen subtree by a randomly
  generated (sub)tree

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GP crossover

• Exchange randomly selected subtrees in the parents

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GP selection

• Standard GA selection is usual
• Sometimes overselection to increase efficiency
• rank population by fitness and divide it into two
  groups
• group 1 best c of population
• group 2 other 100-c
• when executing selection
• 80 of selection operations chooses from group 1
• 20 from group 2
• for pop. size 1000, 2000, 4000, 8000 the
  portion c is
• c 32, 16, 8, 4
• s come from rule of thumb

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Beyond dialects

• Field merging from the early 1990s
• No hard barriers between dialects, many hybrids,
  outliers
• Choice for dialect should be motivated by given
  problem
• Best practical approach choose representation,
  operators, pop. model pragmatically (and end up
  with an unclassifiable EA)
• There are general issues for EC as a whole

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General issues

• WHAT
• WHEN
• WHY
• WHO
• WHERE

is an evolutionary algorithm ? (HC, SA, TS)
does it work ? (problem X, setup Y, performance Z)
does it work ? (Markov chains, schema theory, BBH)
invented evolutionary algorithms first ?
(Turing, Fogel, Holland, Schwefel, )
are we going next for a nice conference ?
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The end